Question

Fill in the blanks.

For r_____ , the sequence $\left\{r^k\right\}$converges to _____.

Short answer

The required answer is for $r=1$, the sequence $\left\{r^k\right\}$converges to 1 and for $\left|r\right|<1$, the sequence converges to 0.

Step-by-step solution

Step 1. Given Information 

The given data is that geometric sequence converges.

Step 2. Explanation 

Using the concept of convergence and divergence of Geometric series.

Let ${\left\{r^k\right\}}_{k=0}^{\infty }$be a geometric sequence. Then for $r=1$, the sequence converges to 1 and for $\left|r\right|<1$, the sequence converges to 0.